Strictly speaking, you cannot "suppress" a header or footer. That is Wordperfect terminology which does not really apply.

You can have a different first page for the header and footer. This is a single setting that applies to both in a given section. If a new section is created, it continues this setting from the previous one.
Header/Footer Settings Recap

You can copy the footer from the main footer and paste it into the first-page footer.